Dear Mr. and Mrs. Muthen, I ran the follwoing SEM model including only continuous variables, and one second-order latent factor:

f1 BY i1 i2 i3; f2 BY i4 i5 i6; f3 BY i7 i8 i9; Gen BY f1 f2 f3;

[...]

Out ON Ind Gen f1res f2res f3res;

where Out and Ind are observed variables and f1res, f2res, f3res are the residuals corresponding to f1, f2, f3 constructed according to Mplus FAQ "Regressing on a residual". According to the output I got and to my own thougts, this model seems not identified. However, if I define Type=Random and add Interaction Terms to the model,

then the model terminates fine with no problems at all and the results do make sense. However, I am wondering how trustworthy the results are if the 'main effects model' is not even identified.

Could you give a hint/reference, both intuitively and mathematically, how this is possible? Furthermore, do the results from the 'interacton model' make sense from a statistical viewpoint?(or are they unstable, probably not replicable?)

Alls this occurs if both analysis (the ones with and without interactions) are done with TYPE=RANDOM, ALGORITHM=INTEGRATION, ESTIMATOR=MLR.